Autor: Xiong, Liming - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Hamiltonian Extendable Graphs
Autorzy:: Yang, Xiaojing
Xiong, Liming
Powiązania:: https://bibliotekanauki.pl/articles/32304150.pdf
Data publikacji:: 2022-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Hamiltonian extendable
forbidden subgraph
Opis:: A graph is called Hamiltonian extendable if there exists a Hamiltonian path between any two nonadjacent vertices. In this paper, we give an explicit formula of the minimum number of edges for Hamiltonian extendable graphs and we also characterize the degree sequence for Hamiltonian extendable graphs with minimum number of edges. Besides, we completely characterize the pairs of forbidden subgraphs for 2-connected graphs to be Hamiltonian extendable.
Źródło:: Discussiones Mathematicae Graph Theory; 2022, 42, 3; 843-859
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: 2-Connected Hamiltonian Claw-Free Graphs Involving Degree Sum of Adjacent Vertices
Autorzy:: Tian, Tao
Xiong, Liming
Powiązania:: https://bibliotekanauki.pl/articles/32034090.pdf
Data publikacji:: 2020-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Hamiltonian cycle
degree sum
dominating closed trail
closure
Opis:: For a graph H, define $\overline{\sigma}_2(H)=min\{d(u)+d(v)|uv∈E(H)\}$. Let $H$ be a 2-connected claw-free simple graph of order $n$ with $\delta(H) ≥ 3$. In [J. Graph Theory 86 (2017) 193–212], Chen proved that if $\overline{\sigma}_2(H)≥\frac{n}{2}−1$ and $n$ is sufficiently large, then $H$ is Hamiltonian with two families of exceptions. In this paper, we refine the result. We focus on the condition $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$, and characterize non-Hamiltonian 2-connected claw-free graphs $H$ of order $n$ sufficiently large with $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$. As byproducts, we prove that there are exactly six graphs in the family of 2-edge-connected triangle-free graphs of order at most seven that have no spanning closed trail and give an improvement of a result of Veldman in [Discrete Math. 124 (1994) 229–239].
Źródło:: Discussiones Mathematicae Graph Theory; 2020, 40, 1; 85-106
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: The Ryjáček Closure and a Forbidden Subgraph
Autorzy:: Saito, Akira
Xiong, Liming
Powiązania:: https://bibliotekanauki.pl/articles/31340869.pdf
Data publikacji:: 2016-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: closure
claw-free graph
Hamiltonian graph
perfect matching
traceable graph
Opis:: The Ryjáček closure is a powerful tool in the study of Hamiltonian properties of claw-free graphs. Because of its usefulness, we may hope to use it in the classes of graphs defined by another forbidden subgraph. In this note, we give a negative answer to this hope, and show that the claw is the only forbidden subgraph that produces non-trivial results on Hamiltonicity by the use of the Ryjáček closure.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 3; 621-628
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: On the Independence Number of Traceable 2-Connected Claw-Free Graphs
Autorzy:: Wang, Shipeng
Xiong, Liming
Powiązania:: https://bibliotekanauki.pl/articles/31343185.pdf
Data publikacji:: 2019-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: traceability
independence number
matching number
trail
closure
Opis:: A well-known theorem by Chvátal-Erdőos [A note on Hamilton circuits, Discrete Math. 2 (1972) 111–135] states that if the independence number of a graph G is at most its connectivity plus one, then G is traceable. In this article, we show that every 2-connected claw-free graph with independence number α(G) ≤ 6 is traceable or belongs to two exceptional families of well-defined graphs. As a corollary, we also show that every 2-connected claw-free graph with independence number α(G) ≤ 5 is traceable.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 4; 925-937
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Forbidden Subgraphs for Collapsible Graphs and Supereulerian Graphs
Autorzy:: Liu, Xia
Xiong, Liming
Powiązania:: https://bibliotekanauki.pl/articles/32361726.pdf
Data publikacji:: 2022-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: forbidden subgraph
supereulerian
collapsible
Opis:: In this paper, we completely characterize the connected forbidden subgraphs and pairs of connected forbidden subgraphs that force a 2-edge-connected (2-connected) graph to be collapsible. In addition, the characterization of pairs of connected forbidden subgraphs that imply a 2-edge-connected graph of minimum degree at least three is supereulerian will be considered. We have given all possible forbidden pairs. In particular, we prove that every 2-edge-connected noncollapsible (or nonsupereulerian) graph of minimum degree at least three is Z₃-free if and only if it is K₃-free, where Z_i is a graph obtained by identifying a vertex of a K₃ with an end-vertex of a P_i+1.
Źródło:: Discussiones Mathematicae Graph Theory; 2022, 42, 2; 417-442
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

Tytuł:: Large Degree Vertices in Longest Cycles of Graphs, I
Autorzy:: Li, Binlong
Xiong, Liming
Yin, Jun
Powiązania:: https://bibliotekanauki.pl/articles/31340944.pdf
Data publikacji:: 2016-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: longest cycle
large degree vertices
order
connectivity
independent number
Opis:: In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 2; 363-382
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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